Satellite communications were incorporated into the fold of 3rd generation partnership project (3GPP) with a goal to expand cellular connectivity worldwide. The aim remains to cover everyone with a broadband-like 5th generation (5G) non-terrestrial network (NTN) and connect everything with an Internet-of-Things (IoT)-based NTN. Several challenges associated with incorporating flying base stations in a cellular network have already been addressed by the wireless research community. A major issue that lingers is the basic one of expanding coverage. Given that satellites are several orders of magnitude farther away from a cellular device than a cell tower is in a terrestrial network, coverage enhancement for NTN is more challenging than for its terrestrial counterpart. In this paper, we explore the challenges of coverage enhancement and the progress that has been achieved to this end.